/***************************************************************************
 *   Copyright (c) 2019 Viktor Titov (DeepSOIC) <vv.titov@gmail.com>       *
 *                                                                         *
 *   This file is part of the FreeCAD CAx development system.              *
 *                                                                         *
 *   This library is free software; you can redistribute it and/or         *
 *   modify it under the terms of the GNU Library General Public           *
 *   License as published by the Free Software Foundation; either          *
 *   version 2 of the License, or (at your option) any later version.      *
 *                                                                         *
 *   This library  is distributed in the hope that it will be useful,      *
 *   but WITHOUT ANY WARRANTY; without even the implied warranty of        *
 *   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the         *
 *   GNU Library General Public License for more details.                  *
 *                                                                         *
 *   You should have received a copy of the GNU Library General Public     *
 *   License along with this library; see the file COPYING.LIB. If not,    *
 *   write to the Free Software Foundation, Inc., 59 Temple Place,         *
 *   Suite 330, Boston, MA  02111-1307, USA                                *
 *                                                                         *
 ***************************************************************************/

#ifndef FREECAD_BASE_DUAL_QUATERNION_H
#define FREECAD_BASE_DUAL_QUATERNION_H

#include "DualNumber.h"


namespace Base {
    /**
     * @brief The DualQuat class represents a dual quaternion, as a quaternion of
     * dual number components. Dual quaternions are useful for placement
     * interpolation, see pow method.
     *
     * Rotation is stored as non-dual part of DualQ. Translation is encoded into
     * dual part of DualQuat:
     * DualQuat.dual() = 0.5 * t * r,
     * where t is quaternion with x,y,z of translation and w of 0, and r is the
     * rotation quaternion.
     */
    class DualQuat {
    public:
        DualNumber x;
        DualNumber y;
        DualNumber z;
        DualNumber w;

    public:
        ///default constructor: init with zeros
        DualQuat() {}

        DualQuat(DualNumber x, DualNumber y, DualNumber z, DualNumber w)
            : x(x), y(y), z(z), w(w) {}

        DualQuat(double x, double y, double z, double w, double dx, double dy, double dz, double dw)
            : x(x, dx), y(y, dy), z(z, dz), w(w, dw) {}

        DualQuat(double x, double y, double z, double w)
            : x(x), y(y), z(z), w(w) {}

        ///Builds a dual quaternion from real and dual parts provided as pure real quaternions
        DualQuat(DualQuat re, DualQuat du);

        ///returns dual quaternion for identity placement
        static DualQuat identity() { return DualQuat(0.0, 0.0, 0.0, 1.0); }

        ///return a copy with dual part zeroed out
        DualQuat real() const { return DualQuat(x.re, y.re, z.re, w.re); }

        ///return a real-only quaternion made from dual part of this quaternion.
        DualQuat dual() const { return DualQuat(x.du, y.du, z.du, w.du); }

        ///conjugate
        DualQuat conj() const { return DualQuat(-x, -y, -z, w); }

        ///return vector part (with scalar part zeroed out)
        DualQuat vec() const { return DualQuat(x, y, z, 0.0); }

        ///magnitude of the quaternion
        double length() const { return sqrt(x.re * x.re + y.re * y.re + z.re * z.re + w.re * w.re); }

        ///angle of rotation represented by this quaternion, in radians
        double theta() const { return 2.0 * atan2(vec().length(), w.re); }

        ///dot product between real (rotation) parts of two dual quaternions (to determine if one of them should be negated for shortest interpolation)
        static double dot(DualQuat a, DualQuat b);

        ///ScLERP. t=0.0 returns identity, t=1.0 returns this. t can also be outside of 0..1 bounds.
        DualQuat pow(double t, bool shorten = true) const;

        DualQuat operator-() const { return DualQuat(-x, -y, -z, -w); }

        //DEBUG
        //void print() const {
        //    Console().Log("%f, %f, %f, %f; %f, %f, %f, %f", x.re,y.re,z.re,w.re, x.du,y.du,z.du, w.du);
        //}
    };

    DualQuat operator+(DualQuat a, DualQuat b);
    DualQuat operator-(DualQuat a, DualQuat b);
    DualQuat operator*(DualQuat a, DualQuat b);

    DualQuat operator*(DualQuat a, double b);
    DualQuat operator*(double a, DualQuat b);
    DualQuat operator*(DualQuat a, DualNumber b);
    DualQuat operator*(DualNumber a, DualQuat b);
} //namespace

#endif
